United Technologies CEO Greg Hayes is in a bind -- and Rolls-Royce may be just the thing to get him out of it.

Hayes has rebuffed takeover advances from rival Honeywell, which last week detailed a cash-and-stock offer that valued United Technologies at $108 a share, or more than $100 billion including debt. He says antitrust and customer opposition would be too great, and that the current offer undervalues United Technologies, anyway. Hayes may have a point on that last one, but if Honeywell were to raise its bid, the other arguments may start to sound self-serving.

It was Hayes that reportedly kicked off talks last year, though the merger discussed then would have left United Technologies management in charge. (Honeywell wants to put CEO Dave Cote in control). United Technologies says the regulatory environment has shifted dramatically in the last year. Well, one thing that's definitely shifted is its stock price, which had fallen almost 30 percent in the year before news of Honeywell's approach broke. Hayes needs to spin a more compelling narrative to convince investors that slump won't resume.

Getting a Boost

News of Honeywell's interest has helped United Technologies reverse some of its stock slump. That won't last if the acquirer goes away.

Source: Bloomberg

A tie-up with U.K. aircraft engine maker Rolls-Royce could be the poison pill he needs to evade Honeywell's clutches. How so? For starters, United Technologies would be bidding at bargain prices. Following a succession of profit warnings, Rolls-Royce's stock has fallen about 27 percent over the past year, cutting its market value to just 12.5 billion pounds ($17.4 billion).

That's still a large transaction, but United Technologies can afford it. While the maker of Otis elevators has earmarked a big chunk of the proceeds from the $9 billion sale of its Sikorsky helicopter business for share repurchases, it's also sitting on a lot of cash parked overseas.

Better Together

Could Rolls-Royce be a better partner for United Technologies?

The strategic logic is what really makes this combination intriguing, though. Rolls-Royce, led by CEO Warren East, is a leader in the wide-body aircraft engines that United Technologies lacks. By contrast, the acquirer has a strong position in the market for single-aisle jet engines -- a big hole for Rolls-Royce, as Gadfly has noted. Together, the two would be an aircraft-engine powerhouse, enabling United Technologies to better challenge General Electric in the market and Rolls-Royce to get out of the hole it's dug for itself.

Wide-body Battle

Rolls-Royce and GE dominate the engine market for new twin-aisle aircraft

Source: Bloomberg Intelligence, Ascend

Nb. CFM is a JV of GE and France's Safran. Pratt & Whitney's market share is due to aircraft already in service.

Rolls-Royce backed out of a single-aisle jet engine joint venture led by United Technologies' Pratt & Whitney aerospace arm in 2012, selling its stake for $1.5 billion. It now finds itself virtually locked out of that high-volume, fast-growing market for at least a decade. That's because Boeing and Airbus have only recently launched new fuel-efficient single-aisle planes and have already decided what engines they want to use.

Narrow-body Competitors

GE and P&W are strongest in the market for single aisle plane engines

Source: Bloomberg Intelligence, Ascend

Nb. CFM is a JV of GE and Safran

Rolls-Royce's best shot at breaking back in on its own is a new geared, fuel-efficient engine called the UltraFan that it's currently investing in heavily. Not only does United Technologies' Pratt & Whitney aerospace arm already have a strong position in single-aisle jets, it also has a geared turbofan design. Teaming up might spare Rolls-Royce's engineers effort and shareholders cash.

It's not a slam dunk. A deal between Rolls-Royce and United Technologies would attract close scrutiny from antitrust authorities. But major customers Airbus and Boeing could hardly complain about a lack of competition in civilian aircraft engines when they already have what is effectively a duopoly in commercial aircraft. Airbus and Boeing might even benefit from having a stronger rival to GE and that company's joint venture with France's Safran, CFM International.

The U.K. government also holds a "golden share" and could block a takeover on national security grounds. (Rolls-Royce has a nuclear power and submarine propulsion business). An approach for a national industrial icon would be especially politically explosive in a year when Britain is considering exiting the European Union.

A safer strategy for United Technologies could be to propose a joint-venture in aerospace engines. Zafar Khan, an analyst at Societe Generale, told clients in January that a joint venture of Pratt & Whitney and Rolls-Royce's civil aerospace and defense activities would make a "great deal of business sense.'' P&W generated $14.1 billion in sales last year compared to sales of about 8.9 billion pounds ($11.4 billion) at Rolls-Royce's civilian and defense aerospace units.

Taking on GE

A joint-venture of Pratt & Whitney and Rolls-Royce aircraft engine activities would create a new leader in civilian and defense aircraft engines

Source: Bloomberg data (inspired by Societe Generale analysis)

United Technologies CEO Hayes has backed away from talk about large deals after his company repeatedly had to cut its own earnings forecasts in 2015. The entrance of Honeywell means he's got to act sooner rather than later to create shareholder value. Rolls-Royce isn't the only possible target, and other options for Hayes could include a major breakup of the aerospace operations and building systems businesses.

There's certainly a lot to like, though. It might be worth a call to Rolls-Royce's East.

This column does not necessarily reflect the opinion of Bloomberg LP and its owners.